Quadrature domains and kernel function zipping

It is proved that quadrature domains are ubiquitous in a very strong sense in the realm of smoothly bounded multiply connected domains in the plane. In fact, they are so dense that one might as well assume that any given smooth domain one is dealing with is a quadrature domain, and this allows access to a host of strong conditions on the classical kernel functions associated to the domain. Following this string of ideas leads to the discovery that the Bergman kernel can be zipped down to a strikingly small data set. It is also proved that the kernel functions associated to a quadrature domain must be algebraic.Comment: 13 pages, to appear in Arkiv for matemati

Comment on "Separability of quantum states and the violation of Bell-type inequalities"

The statement of E.R. Loubenets, Phys. Rev. A 69, 042102 (2004), that separable states can violate classical probabilistic constraints is based on a misleading definition of classicality, which is much narrower than Bell's concept of local hidden variables. In a Bell type setting the notion of classicality used by Loubenets corresponds to the assumption of perfect correlations if the same observable is measured on both sides. While it is obvious that most separable states do not satisfy this assumption, this does not constitute "non-classical" behaviour in any usual sense of the word.Comment: 1 page, accepted by Phys. Rev.

Submerged dunes and breakwater embayments mapped using wave inversions of shore-mounted marine X-Band radar data

Surveying very shallow coastal areas, particularly around coastal defences, can be a logistically difficult and time consuming process. A marine-radar based bathymetry mapping technique has been used to remotely map the embayments around a series of shore-parallel breakwaters at Sea Palling on the south east coast of England during the LEACOAST2 project. The duration of the deployment spanned over 2 years, with the aim of observing any evolution of bathymetric features over that timescale while providing a clear indication of the spatial variability of wave and current patterns contributing to such evolution. The embayments generated by the shore parallel breakwaters at that site are resolved and a field of subtidal dunes with a wavelength of the order of 200m and amplitude around 1m located in approximately 6-10m of water were within the radar field of view and are evident in the remotely sensed bathymetry. Comparisons between bathymetric data obtained using conventional survey techniques and the radar based technique are presented together with measurements of tidal currents mapped using the same remote sensing method and compared with ADCP data during a storm even

Three Conceptual Themes for Future Research on Teams

[Excerpt] Tannenbaum, Mathieu, Salas, and Cohen (2011) identify three change themes – dynamic composition, technology/distance, and delayering/empowerment – that are affecting the nature of teams and discuss future research directions within each thematic area. They acknowledge that these emerging research needs may require new theories, research methods, and analyses and describe a few specific approaches that may hold promise, but focus their attention largely on describing the substantive issues and questions research should target going forward. We do not dispute that these themes are important – they are garnering substantial research attention (see Bell, 2007; Chen & Tesluk, in press; Kirkman, Gibson, & Kim, in press). However, they are among many issues that are in flux and important to consider in future research on teams. In this commentary, we adopt a broader perspective aimed at highlighting several conceptual, rather than substantive, themes that we believe can focus and leverage future research on the changing nature of teams. These conceptual themes are: (1) multilevel influences, (2) emergence, and (3) temporal dynamics. Sophisticated research questions and designs that encompass these conceptual issues will advance our understanding of the themes identified by Tannenbaum et al. (2011) as well as other emerging issues surrounding teams. In the following sections, we describe the three conceptual themes and then highlight the implications of these themes for future research on the changing nature of teams

Correlation functions, Bell's inequalities and the fundamental conservation laws

I derive the correlation function for a general theory of two-valued spin variables that satisfy the fundamental conservation law of angular momentum. The unique theory-independent correlation function is identical to the quantum mechanical correlation function. I prove that any theory of correlations of such discrete variables satisfying the fundamental conservation law of angular momentum violates the Bell's inequalities. Taken together with the Bell's theorem, this result has far reaching implications. No theory satisfying Einstein locality, reality in the EPR-Bell sense, and the validity of the conservation law can be constructed. Therefore, all local hidden variable theories are incompatible with fundamental symmetries and conservation laws. Bell's inequalities can be obeyed only by violating a conservation law. The implications for experiments on Bell's inequalities are obvious. The result provides new insight regarding entanglement, and its measures.Comment: LaTeX, 12pt, 11 pages, 2 figure

On the dimension of H-strata in quantum matrices

We study the topology of the prime spectrum of an algebra supporting a rational torus action. More precisely, we study inclusions between prime ideals that are torus-invariant using the $H$-stratification theory of Goodearl and Letzter on one hand and the theory of deleting derivations of Cauchon on the other. We apply the results obtained to the algebra of $m \times n$ generic quantum matrices to show that the dimensions of the $H$-strata described by Goodearl and Letzter are bounded above by the minimum of $m$ and $n$, and that moreover all the values between 0 and this bound are achieved.Comment: New introduction; results improve

Bell's theorem as a signature of nonlocality: a classical counterexample

For a system composed of two particles Bell's theorem asserts that averages of physical quantities determined from local variables must conform to a family of inequalities. In this work we show that a classical model containing a local probabilistic interaction in the measurement process can lead to a violation of the Bell inequalities. We first introduce two-particle phase-space distributions in classical mechanics constructed to be the analogs of quantum mechanical angular momentum eigenstates. These distributions are then employed in four schemes characterized by different types of detectors measuring the angular momenta. When the model includes an interaction between the detector and the measured particle leading to ensemble dependencies, the relevant Bell inequalities are violated if total angular momentum is required to be conserved. The violation is explained by identifying assumptions made in the derivation of Bell's theorem that are not fulfilled by the model. These assumptions will be argued to be too restrictive to see in the violation of the Bell inequalities a faithful signature of nonlocality.Comment: Extended manuscript. Significant change

Quantum interference and non-locality of independent photons from disparate sources

We quantitatively investigate the non-classicality and non-locality of a whole new class of mixed disparate quantum and semiquantum photon sources at the quantum-classical boundary. The latter include photon added thermal and photon added coherent sources, experimentally investigated recently by Zavatta et al. [Phys. Rev. Lett. 103, 140406 (2009)]. The key quantity in our investigations is the visibility of the corresponding photon-photon correlation function. We present explicit results on the violations of the Cauchy-Schwarz inequality - which is a measure of nonclassicality - as well as of Bell-type inequalities.Comment: 9 pages, 3 figure

Monogamy of Bell's inequality violations in non-signaling theories

We derive monogamy relations (tradeoffs) between strengths of violations of Bell's inequalities from the non-signaling condition. Our result applies to general Bell inequalities with an arbitrary large number of partners, outcomes and measurement settings. The method is simple, efficient and does not require linear programming. The results are used to derive optimal fidelity for asymmetric cloning in nonsignaling theories.Comment: 4 pages, 2 figures, published versio